Conductors, Insulators, and Semiconductors
Source lecture(s): SC134 Lec1
Intuition
Materials respond to electric fields differently depending on how freely charges can move.
Formal Definition
Conductors have free charge carriers; insulators do not; semiconductors are intermediate and tunable.
Mathematical Formulation
Current density: \(\vec{J} = nq\vec{v}_d\) Resistivity: \(\rho = E/J\)
Derivation
Drude model treats conduction electrons as a gas; Ohm's law emerges from average drift under \(E\).
Worked Example
Copper: \(\sigma\approx 5.8\times10^7\,\text{S/m}\). Silicon: tunable from \(10^{-3}\) to \(10^4\,\text{S/m}\).
Common Mistakes
- Confusing conductivity (\(\sigma\)) with resistivity (\(\rho\)).
- Assuming superconductors have zero resistance only at room temperature.
Related Concepts
Quiz
Q1. Which class has tunable conductivity?
Answer
Semiconductors.